Match each condition to the number of triangles that can be constructed to fit the condition. condition A: one side
measuring 4 inches,
another side measuring
8 inches, and a third
side measuring 10 inches
condition B: one angle
measuring 60°, another
angle measuring 40°, and
a third angle measuring 90°
condition C: one side
measuring 4 inches,
another side measuring
8 inches, and the angle
between them measuring 70°
condition D: one side
measuring 5 inches,
another side measuring
7 inches, and a third
side measuring 12 inches
condition E: one angle
measuring 30°, another
angle measuring 80°,
and the length of the
included side measuring
8 inches
condition F: one angle
measuring 40°, another
angle measuring 80°, and
a third angle measuring 60°

Deere & Company (DE)

1. Calculation of Ratios:

a) Return on total assets = Net income divided by the average total assets, multiplied by 100.

Year 3  = $1,523.9/$57,965 x 100 = 2.6%

Year 2  = $1,940.0/$ 59,642 x 100 = 3.3%

Year 1 =  $3,161.7 /$ 60,429  x 100 = 5.2%

b) Return on stockholders' equity: Earnings after taxes/Stockholders' equity x 100.

Year 3  = $1,523.9/$ 6,644  x 100 = 22.9%

Year 2  = $1,940.0/$7,912 x 100 = 24.5%

Year 1 =  $3,161.7 /$ 9,667  x 100 = 32.7%

c) Earnings per share: Net Income/No. of outstanding shares.

Year 3  = $1,523.9/315 = $4.84

Year 2  = $1,940.0/334 = $5.81

Year 1 =  $3,161.7 /363 = $8.71

d) Dividend yield:  This is equal to the annual dividend per share divided by stock price per share, and multiplied by 100.

Year 3  = $2.40/$92.03 x 100 = 2.61%

Year 2  = $2.40/$81.10 x 100 = 2.96%

Year 1 = $2.22/$85.58 x 100 = 2.59%

e) Price-earnings ratio:  This is equal to market price per share divided by the earnings per share.

Year 3  = $92.03/$4.84 = 19.0 times

Year 2  = $81.10/$5.81 = 13.9 times

Year 1 = $85.58/$8.71 = 9.8 times

Explanation:

a) Data

                                                Year 3          Year 2         Year 1

                                               ('millions)     ('millions)     ('millions)

Net income (loss)                   $1,523.9       $1,940.0     $3,161.7

Preferred dividends                    $ 0.00          $ 0.00       $ 0.00

Interest expense                      $763.7        $ 680.0     $ 664.0

Shares outstanding                    315              334            363

for computing earnings per share

Cash dividend per share          $ 2.40      $ 2.40        $ 2.22

Average total assets             $57,965    $ 59,642     $ 60,429

Average stockholders' equity  $ 6,644     $7,912       $ 9,667

Average stock price per share  $ 92.03   $ 81.10      $ 85.58

b) Return on total assets = Net income divided by the average total assets, multiplied by 100.  It shows how well a company generates net income from assets.

Year 3  = $1,523.9/$57,965 x 100 = 2.63%

Year 2  = $1,940.0/$ 59,642 x 100 = 3.25%

Year 1 =  $3,161.7 /$ 60,429  x 100 = 5.23%

c) Return on stockholders' equity: Earnings after taxes/Stockholders' equity x 100.  It demonstrates how much of the earnings after taxes are available to stockholders.

Year 3  = $1,523.9/$ 6,644  x 100 = 22.94%

Year 2  = $1,940.0/$7,912 x 100 = 24.52%

Year 1 =  $3,161.7 /$ 9,667  x 100 = 32.71%

d) Earnings per share: Net Income/No. of outstanding shares.  It shows in dollar terms how much of the earnings made by a company is available to stockholders on the average of each share.

Year 3  = $1,523.9/315 = $4.84

Year 2  = $1,940.0/334 = $5.81

Year 1 =  $3,161.7 /363 = $8.71

e) Dividend yield:  This is equal to the annual dividend per share divided by stock price per share, and multiplied by 100.  It shows how a company pays dividend each year in relation to its share price.

Year 3  = $2.40/$92.03 x 100 = 2.61%

Year 2  = $2.40/$81.10 x 100 = 2.96%

Year 1 = $2.22/$85.58 x 100 = 2.59%

f) Price-earnings ratio:  This is equal to market price per share divided by the earnings per share.  It shows if a company is overvalued or undervalued.

Year 3  = $92.03/$4.84 = 19.0 times

Year 2  = $81.10/$5.81 = 13.9 times

Year 1 = $85.58/$8.71 = 9.8 times

g) Ratios are used to present a picturesque view of a company's financial performance and position to make easily understood and compared with other companies in the industry and over the years (trend analysis).  They are important financial management and investment tools, which should, however, not be taken in isolation.